Problem: $\lim_{x\to {\frac{\pi}{3}}}\sin(x)=?$ Choose 1 answer: Choose 1 answer: (Choice A) A $\dfrac{1}{2}$ (Choice B) B $\dfrac{\sqrt{3}}{2}$ (Choice C) C $\sqrt{3}$ (Choice D) D The limit doesn't exist.
Answer: $\sin(x)$ is continuous on all points in its domain, and its domain is all real numbers. Therefore, we can find $\lim_{x\to {\frac{\pi}{3}}}\sin(x)$ by direct substitution. $\begin{aligned} \sin\left(\dfrac{\pi}{3}\right)&=\dfrac{\sqrt{3}}{2} \end{aligned}$ $\lim_{x\to {\frac{\pi}{3}}}\sin(x)=\dfrac{\sqrt{3}}{2}$